Length of fence = Circumference of the pool – width of the gate. Length of fence = 6.28x – 150 cm.
What is the length of the fence?Let the circular pool has the radius (r ) = x cm.Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.Length of fence = Circumference of the pool – width of the gate.Length of fence = 2 π r – 150Length of fence = 2 × 3.14 × x – 150Length of fence = 6.28x – 150 cm.a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius.To learn more about length of the fence refers to:
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Use the binomial theorem to expand expressions 1-4 and answer question 5.
1. (3x^2 +y)^3
2. (5x^4 +2y^5)^4
3. (x^3 +4y^2)^5
4. (x-2y)^6
5. find the coefficient of x^3 y^4 in the expansion of (2x+5y^2)^5
On solving the provided question, we cans ay that the value of x from the polynomial [tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex] is = 16 and 1
what are polynomials?A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.
here,
[tex]5x^4 +2y^5)^4[/tex] and [tex](3x^2 +y)^3[/tex]
as x = 0 and y = 1
answer is = 16 and 1
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-√8 - √54 + 2√6 how to simplify
Answer:
6√2
Step-by-step explanation:
-√2×2×2 -√2×3×3×3 + 2√3×3
-2√2 - 3✓6 + 2×3
-2√2 - 3√2×2 +2 + 6
6√2
Katerina needs 200 balloons fillied with helium for a party. She knows that each balloon will need 0.7ft^3 of helium. the helium canisters hold 0.20m^3. 1m^3 = 35ft^3. How many Canisters will Katerina need to buy?
=======================================================
Explanation:
1 balloon = 0.7 ft^3 of helium
200 balloons = 200*0.7 = 140 ft^3 of helium
Katerina needs 140 cubic feet of helium to fill all 200 balloons.
---------------
1m^3 = 35ft^3 which is approximate
0.2 m^3 = 0.2*35 = 7 ft^3
Each canister holds approximately 7 cubic feet of helium.
----------------
To summarize so far.
Katerina needs 140 cubic feet of helium.Each canister holds approximately 7 cubic feet of helium.Let x be the number of canisters. Because of fact 2 mentioned above, 7x represents the total amount of helium from all of the x number of canisters.
Set this equal to the amount she needs (140) and solve for x.
7x = 140
x = 140/7
x = 20
Katerina needs 20 canisters.
the graph of a function f is the collection of ____________ or (x,f(x)) such that x is in the domain of f
4 is the slope of a line y - 4x = 0 true or false
it is false but 4 is not y-4x=0
Need it ASAP, please!!!
Answer:
27y - 45 + 7z
Please screenshot and write the answer on the photo.
1] Answer: y = -[tex]\frac{1}{2}[/tex]x + 3
Step-by-step explanation:
➜ This line is going down from the top left to the bottom right, so it will have a negative slope.
➜ Using rise over run, we get a slope of -2/4. This simplifies to -1/2.
➜ The line intercepts the y-axis at 3.
2] Answer: y = 3x
Step-by-step explanation:
➜ This line is going down from the bottom left to the top right, so it will have a positive slope.
➜ Using rise over run, we get a slope of 3/1. This simplifies to 3.
➜ The line intercepts the y-axis at 0.
3] Answer: y = x - 4
Step-by-step explanation:
➜ This line is going down from the top left to the bottom right, so it will have a negative slope.
➜ Using rise over run, we get a slope of 2/2. This simplifies to 1.
➜ The line intercepts the y-axis at -4.
You deposit $250 in an account that earns simple interest at an annual rate of 2.2%.
How much money is in the account after 4 years?
Answer: $272
Step-by-step explanation: you would multiply 250 * 0.022 = 5.5
then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272
Verify which of the following are identities. 1) 1 + = 4 sec 2) 15 cos = 15 a. Only the first equation is an identity. b. None of the equations are identities. c. Only the second equation is an identity. d. Both the equations are identities. Please select the best answer from the choices provided A B C D
The correct option regarding which of the sentences represents a trigonometric identity is given as follows:
b. None of the equations are identities.
What is a trigonometric identity?A trigonometric identity is a relation that is true for all possible angle measures of [tex]\theta[/tex]
The first relation is given as follows:
[tex]4\cos{\theta}\tan{\theta}\sec{\theta} = 4[/tex]
The tangent and secant equations are given as follows:
tan(x) = sin(x)/cos(x).sec(x) = 1/cos(x).Hence:
4cos(x)tan(x)sec(x) = 4cos(x) x sin(x)/cos(x) x 1/cos(x)
4cos(x)tan(x)sec(x) = 4sin(x)/cos(x)
4cos(x)tan(x)sec(x) = 4tan(x).
Meaning that the first statement is not an identity.
The second relation is given as follows:
[tex]\frac{9\sec^{2}{\theta}}{\cos^{2}{\theta}} - \frac{\tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
With a single denominator, we have that:
[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
The secant identity is given as follows:
[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]
Hence:
[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
[tex]\frac{9(1 + \tan^2{\theta}) - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
[tex]\frac{9 + 8\tan^2{\theta}}{\cos^{2}{\theta}} = 2[/tex]
Is also a false statement, hence neither is an identity and option B is correct.
Missing InformationThe statements are given by the image presented at the end of the answer.
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There is a proportional relationship between the weight and total cost of a bag of lemons. One bag weighs 2.4 pounds and costs $5.28. Another bag weighs 2.7 pounds and costs $5.94. Describe how you would graph the proportional relationship i need help asp
There is a directly proportional relationship between the weight and total cost of bag of of lemons.
What is constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
When two variables are directly or indirectly proportional to one another, their relationship may be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant.
Given data :
One bag weighs 2.4 pounds and cost $5.28.
Another bag weighs 2.7 pounds and cost $5.94
2.4k = 5.28
k= 2.2
2.7k = 5.94
k = 2.2
k > 1
The weight and total cost of bag of of lemons is directly proportional, so when weight of lemon increases, the cost of lemon also increases.
Therefore, there is a directly proportional relationship between the weight and total cost of bag of of lemons.
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An Item costs $450 Before tax. and the sales tax is $31.50
Find the sales tax rate. Write your answer as a percentage
The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%
What is tax rate?The tax rate is the percentage of an income or an amount of money that has to be paid as tax.
To find the tax rate of $31.50 from $450
The formula is
Amount taxed/Principal amount x 100
= $31.50/$450 x100
=$3150/450
=7%
Hence, the tax rate is 7%
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Determine whether the statement is true or false. If false, give a counterexample.
The constant of proportionality in an equation can never be 0.
Answer:
Step-by-step explanation:
Helpp!! Solve the system by graphing.
what is the cosine of π/3
7 - 13a = 27 solve for A
Answer:
a = -20/13
Step-by-step explanation:
7 - 13a = 27
-13a = 20
a = -20/13
Let's check
7 - 13(-20/13) = 27
7 + 260/13 = 27
7 + 20 = 27
27 = 27
So, a = -20/13 is the correct answer!
Please help I don’t understand this
On solving the provided question, we can say that - the area of the following rectangle is 200 cm sq.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
we have
L = 20 cm
and B = 10 cm
Area of rectangle, A =L X B = 20 X 10 = 200 cm sq.
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Roller coaster A can reach a top speed of 110 ft./s roller coaster B can reach a top speed of 85 mph which roller coaster has a greater top speed?
Roller coaster B has greater top speed than roller coaster A.
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Given,
speed of roller coaster A = 110ft./s
speed of roller coaster B = 85mph
1 mile = 5280 feet
⇒ 85 mile = 5280 × 85 = 448800 feet
1 hour = 3600 seconds
speed of roller coaster B = 448800/3600 ft/s = 124.67 ft/s
comparing speed of both
Speed of roller coaster B > speed of roller coaster A
Hence roller coaster B has greater top speed.
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Every time an insect jump forward the distance covered is half of previous jump. if the insect initially jumped 8.4cm calculate to the nearest two decimal places distance of sixth jump
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
What is a geometric sequence?Let a₁ be the first term and r be the common ratio.
Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
Every time an insect jump forward, the distance covered is half of the previous jump. If the insect initially jumped 8.4 cm.
The equation is given as,
aₙ = 8.4 · (1/2)ⁿ⁻¹
The distance that he jumped in the sixth jump will be given as,
a₆ = 8.4 · (1/2)⁶⁻¹
a₆ = 8.4 / 64
a₆ = 0.13125
a₆ ≈ 0.13
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
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Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
Find P(5) when μ = 9
Answer: 0.155
Step-by-step explanation:
To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:
P(k) = (μ^k * e^(-μ)) / k!
Where:
P(k) is the probability of the event occurring k timesμ is the meane is the base of the natural logarithm ( approximately 2.71828)k! is the factorial of k (k factorial)Plugging in the given values, we get:
P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550
So the probability of the event occurring 5 times is approximately 15.5%.
WHAT IS A PRICE OF A 7 - MINUTE DIAL DIRECT CALL TO NEW YORK, NY, WHEN YOU
CALL IN THE EVENING?
The price of a seven minute call direct to New York, in the evening, is given as follows:
$5.82.
How to obtain the cost of the call?The cost of the call is obtained considering the information given in the table, for which the proportions are applied.
We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.
Then the minute proportions, considering that the call happens in the evening, are given as follows:
First minute: 0.38 of $3.Each additional minute: 0.26 of $3.A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:
0.38 x 3 + 6 x 0.26 x 3 = $5.82.
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What is the solution to the system of equations?
{x+y=4
{x=y=1
O (3, 1)
O (2, 2)
O (1/2, 3/2)
Answer:
hat are the solution(s) to the system of equations shown below? x2 + y2 = 5 y = 2x. 1) x = 1 and x = −1. 2) x = 1. 3) (1,2)
Step-by-step explanation:
Therefore , the solution of the given problem of linear equation comes out to be (2,2).
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
=> y+ x = 3
=> y= 3-x
=> x= y = 1
=>3-x =1
=> x = 2
=> y = 2
(2,2)
Therefore , the solution of the given problem of linear equation comes out to be (2,2).
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(100 points) Need help asap!
The function f(x) is defined below. What is the end behavior of f(x)?
[tex]f(x)=\frac{1}{9} x^{12}[/tex]
A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞
The function f(x) is defined below. What is the end behavior of f(x)?
[tex]f(x)=-\frac{1}{10} x^{18}[/tex]
A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞
The end behavior of the function f(x) = 1/9 x¹² is
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞The end behavior of the function f(x) = -1/10 x¹⁸ is
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of functionThe given function is:
f(x) = 1/9 x¹²
The positive exponents will mean that x will always yield positive values hence f(x) is always positive
f(x) = -1/10 x¹⁸
The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative
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Susan invested a total of $9000 in two accounts. One account pays 3% interest and the other account pays 6% interest. The total return from both accounts was $450.
The money invested in a account with 3% interest is $3000 and the money invested in a account with 6% interest is $6000.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.
Given that, Susan invested a total of $9000 in two account.
One account pays 3% interest and the other account pays 6% interest.
Let the money invested in a account with 3% interest be x.
Then, the money invested in a account with 6% interest be 9000-x.
The total return from both accounts was $450.
Here, (x×3×1)/100 + ((9000-x)×6×1)/100 =450
3x+54000-6x=45000
54000-3x=45000
3x=9000
x=$3000
So, 9000-x=$6000
Therefore, the money invested in a account with 3% interest is $3000 and the money invested in a account with 6% interest is $6000.
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7. A group of friends orders pizza at a restaurant. Each person gives some money to Chris before they order.
a. Chris has $63 to spend on the order, including tax. The tax at the restaurant is 5%. What is the maximum cost of food the group can order and not go over $63? Explain your reasoning.
b. Chris wants to leave a 15% tip on the price of the food, calculated before sales tax. What is the maximum cost of food the group can order and not go over $63? Explain.
(20 points)which of these equations doesn’t fit with each other with what we’ve been learning about perpendicular lines explain why for full credit, equations in photo
Answer:
Line D
Step-by-step explanation:
You want to know which line is not parallel or perpendicular to the other given lines:
A: 2y -x = 2
B: 4y = -8x -4
C: y = -2x +4
D: 5y = 10x +15
Standard formWe can write each of these equations in standard form to make it easier to compare them. That form is ...
ax +by = c
where a > 0 and a, b, c are mutually prime.
The equations are ...
A: x -2y = -2
B: 2x +y = -1
C: 2x +y = 4
D: 2x -y = -3
Parallel linesEquations with the same coefficients of x and y will be parallel:
2x +y = -1 and 2x +y = 4 . . . . lines B and C
Perpendicular linesEquations with coefficients that have been swapped, with one negated, will be perpendicular:
x -2y = -2 and 2x +y = -1 . . . . lines A and B
Line A is perpendicular to parallel lines B and C, so line D is the odd one out.
Line D doesn't fit.
Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars.
0.8d (yes or no)
d – 0.2 (yes or no)
d – 0.2d (yes or no)
1 – 0.2d (yes or no)
7 - Select the equation that represents a true statement.
Mark all that apply.
A. 2+3 × 4 = 22 +12
B. z+zx9 = 9z O
C. -8y + 4.3y + 3.7 = 0
D. 12-1.8b+ 1.8b = 1.8b
E. m8+7(8) = m
So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
A. 2+3 × 4 = 22 +12 is not a true statement, because the order of operations is not followed, multiplication should be done before addition.
B. z+zx9 = 9z is not a true statement, because it is not clear what the operation is between z and x, and what the operation is between x and 9
C. -8y + 4.3y + 3.7 = 0 is a true statement because it is a linear equation with one variable y, it represents a straight line.
D. 12-1.8b+ 1.8b = 1.8b is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.
E. m8+7(8) = m is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.
So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0
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Please help me I can’t figure it out
The number of times each number divides is 8 divides LCM into 11 times
11 divides into LCM 8 times and 22 divides into LCM 4 times .
What is LCM ?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
The LCM of 8 , 11 and 22 is 88
∴ 8 divides into LCM 11 times
11 divides into LCM 8 times
22 divides into LCM 4 times
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Which is 70% of 2,000?
A.14
B.70
C.140
D.700
E.1400
Answer:
Option E) 1400
Step-by-step explanation:
Based on the given conditions, formulate: 70‰ x 2000
Convert the percentage to decimals: 0.7 x 2000
Calculate the product or quotient: 1400
Hence , the answer is 1400
Write the number 4,207 in expanded form
Answer:
That's easy! four thousand two hundred and seven or 4,000+200+7
Step-by-step explanation: